A078954 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,4).

1597, 3907, 12097, 12907, 38317, 58897, 65827, 90007, 90187, 112237, 129277, 134077, 140407, 176317, 204427, 336757, 374977, 390097, 394717, 435637, 486667, 538147, 543997, 588937, 618577, 678637, 702337, 922627, 990277, 996157, 1086247, 1248337, 1326037, 1348537

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+4, p+10, p+12 and p+16 are consecutive primes.

Examples

			90007 is in the sequence since 90007, 90011 = 90007 + 4, 90017 = 90007 + 10, 90019 = 90007 + 12 and 90023 = 90007 + 16 are consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from R. J. Mathar)

Crossrefs

Subsequence of A078851. - R. J. Mathar, Feb 11 2013

Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[85000]],5,1],Differences[#] == {4,6,2,4}&]][[1]] (* Harvey P. Dale, Sep 30 2012 *)

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002